In a small bowl, mix the first six ingredients. Reserve 1 1/3 cups for basting; cover and refrigerate. Divide remaining marinade between two large resealable plastic bags. Add 3 chicken breast to each; seal bags and turn to coat. Refrigerate for 8 hours or overnight.

Drain and discard marinade from chicken. Moisten a paper towel with cooking oil; using long-handled tongs, lightly coat the grilling rack.

Grill chicken, covered, over medium heat for 6-8 minutes or until no longer pink; baste occasionally with reserved marinade during the last 5 minutes.